Related papers: A family of determinants associated with a square …
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and…
We compute the degree complexity of a family of birational mappings of the plane with high order singularities.
We construct a moduli space for the connected subgroups of an algebraic group and the corresponding universal family. Morphisms from an algebraic variety to this moduli space correspond to flat families of connected algebraic subgroups…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some one-parametric eigenvalue problems in dimension one with polynomial potentials.
For an algebraic stack $\sX$ flat and of finite presentation over a scheme $S$, we introduce various notions of {\em relative connected components} and {\em relative irreducible components}. The main distinction between these notions is…
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the $\delta$ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the…
We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields.
In this article we consider the behavior in the vicinity of infinity of the class of all planar quadratic differential systems. This family depends on twelve parameters but due to action of the affine group and re-scaling of time the family…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
We examine the capacity of the complementarity spectrum to distinguish non-isomorphic digraphs. We focus on the seven families with exactly three complementarity eigenvalues. Our findings reveal that in some, but not all families, any two…
3 families of 4-dimensional lattices $L_k, M_k, M_k / 2 \subset \mathbb{R}^2$ are defined. Each lattice is defined by 2 quadratic extensions and has a \emph{finite} number of unit vectors, but the number of unit vectors in each of the 3…
Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
We introduce a family of models, which we name matrix models associated with children's drawings -- the so-called dessin d'enfant. Dessins d'enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky).…
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
We consider infinite parametric families of octic fields, that are quartic extensions of quadratic fields. We describe all relative power integral bases of the octic fields over the quadratic subfields.
In this paper, we are going to calculate the determinant of a certain type of square matrices, which are related to the well-known Cauchy and Toeplitz matrices. Then, we will use the results to determine the rank of special non-square…